A few weeks ago I saw an article in the New York Times, “How to Fix Our Math Education.” The authors suggest replacing the theoretical teaching of math with applicable math. “The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact,” mathematicians Sol Garfunkel and David Mumford wrote in their op-ed piece.
Most people never need to solve the quadratic formula or use complex numbers, so why do we spend so much time teaching so many children math skills they will never use? Sounds rational.
The authors suggest “teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations.” Again, entirely rational and reasonable. Perhaps if people understood math better on a relevant, everyday basis, fewer people would have signed mortgages they could never pay. (I have no proof of this, but I can’t help fantasizing about a couple ridiculing a mortgage broker proposing ludicrous terms.)
Kari Kling teaching a Math Mania class in her home.
I started teaching in 1993 at Aztec Elementary School in Scottsdale. One of the lead teachers responsible for designing the school, Kari Kling, is an expert at making curriculum relevant to students based on how their brains develop. She understands that awareness of the brain development in children should be driving what is presented in the classroom.
In 1997 she published a book called It’s Not About Math, It’s About Life. It relates math to the real world, where it belongs. The authors of the Times article would probably approve of her approach.
Kling says, “We use the language of math to communicate about something in real life. Numbers aren’t just random, they stand for things.” She teaches a class called Math Mania “to teach kids about numbers as a foundational piece so they understand math when it gets more complicated. Kids need to have real experiences with numbers. If they hear something weighs 14 pounds they need to know what 14 pounds feels like.”
When I taught third and fourth graders, we were learning about the Titanic. They read that the doomed ship was 882 feet long. I asked if that was bigger than a football field. Some said yes, some said no. I told them a football field was 300 feet, goal line to goal line. Silence. One kid who understood numbers said, “The Titanic is almost three times the size of a football field?” He was stunned. I asked if they thought the Titanic would fit on our playground. Some said yes, some said no.
Dice for generating sums.
The next day I brought my 100-foot extension cord to measure the playground. By the time we had got to 882 feet, they had a clear sense of how big the Titanic was. Teachers call this number sense and it is what Kling focused her second and third graders on. What good is manipulating numbers in an algorithm if there is no understanding what those numbers mean?
I went to Kling’s house a few weeks ago to watch her teach a Math Mania class for second and third graders. She had the kids come up with as many ways as they could to add two numbers to make 10 as a short cut to adding large columns of numbers. She calls this “bridging to 10.” It yielded a pattern as pictured in the photo at left. Hopefully the student will see the numbers on the left go from 1 to 9 and the numbers in the middle are 9 to 1 and apply this pattern for any sum.
Then they rolled two or three dice and added the numbers to discover what combinations the dice yielded. They kept track of the sums on a chart. In a subsequent class they would analyze which sums came up the most often, which pairs of numbers came up and why.
The kids were all doing math but they were playing with numbers and playing with dice and writing about the activities in their journals. It wasn’t more “kill and drill” of worksheets or page after page of problem sets. They were playing with numbers in their heads, on paper and with other kids.
There are parents who think math doesn’t need to be fun, it has to be learned. But these are kids, and kids — and adults, really — remember things that are fun because so many parts of their brains is being stimulated all at once.
Plus, it’s better to think of math as fun than as a chore.
Story and photos by Daniel Friedman
Students keep track of what number combinations and sums they roll.